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\title{Fall Detection Research Report}   % type title between braces
\author{Guney Kayim}         % type author(s) between braces

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This report is a summary for what I've researched lately over the 'Fall Detection' topic. 

\section{Why?}
\paragraph{}I am interested in this topic because I want to work on a topic that would be helpful for mankind, and I want to pick a topic which is not researched deeply. In other words I want a 'new' topic that I could work on and develop something novel. From the initial research, I've concluded that this topic fulfills my desires as studies, experiments, and trials that could be done over this topic seems open-ended.

\section{Research}
\paragraph{}To gain insight about the topic I read several papers \cite{Anderson2006, Anderson2008, Rougier2011, Rougier2011a, Rougier2009}, and selected one of them \cite{Rougier2009} to work on. I've selected that paper because it is intuitively more easy to understand and implement. Methods, features, and detection approach used on my study is written below. What kind of results achieved are explained shortly.

\subsection{Methods}
\paragraph{}Here are the methods used in order the extract features from the image sequences. Why they are needed is explained.

\subsubsection{Background Estimation}
\paragraph{}Background estimation is used to extract people from the scene, since our focus is humans. Kalman filter based background estimator \cite{Scott} is used. It basically updates the background image by applying Kalman filter on each pixel. Results of this estimator is acceptable but it could become better my optimizing its parameters. Since it is not invariant to illumination differences and shadows (it is not in the implementation I used), some other background estimator(s) could be tried.

\subsubsection{Motion History Image}
\paragraph{}Motion History Image (MHI) is needed to select possible falls from the image sequence. Since MHI occurs when there is a motion, and brightness of the MHI differs depending on largeness of the motion, it is very helpful. It is implemented as described in \cite{Bobick2001}.

\subsubsection{Ellipse Fitting}
\label{subsection_ellipse_fitting}
\paragraph{}Ellipse fitting is used to analyze the shape of humans. Ellipse is fitted on the foreground region extracted using background estimation. Ellipse parameters which we intend to use are the angle between the major axis of the ellipse and horizontal axis ($\theta$) and the ratio of the major axis and minor axis of the ellipse ($\rho$). These parameters are calculated using moments. \emph{It seems like there is some error in calculation of $\rho$ since it was not discriminative in experiments.}

\subsection{Features}
\paragraph{}The data retrieved from the methods are converted into features. 

\subsubsection{Motion Quantity}
\paragraph{}Motion Quantity ($cMotion$) is a feature extracted using both MHI ($H_{\tau}$) and foreground region ($blob$). It is calculated as follows:
\begin{equation}
cMotion = \frac{\sum{_{Pixel(x,y)\in{blob}}H_{\tau}(x,y,t)}}{\#pixels\in{blob}}
\end{equation}
If there is a fast movement in the scene then there will be more MHI pixels in the foreground region and the cMotion value will be larger, or it will be low otherwise. So if $cMotion$ value is high then it can be said that there is a possible fall.

\subsubsection{Standard Deviation of $\theta$}
\paragraph{}There are several approaches to calculate $\sigma_\theta$. Here are some approaches.
\begin{enumerate}
\item Calculate the $\sigma_\theta$ using the $\theta$ values from the past 1 second, whenever a possible fall is detected. This approach is mentioned in \cite{Rougier2009}.
\item Take the $\theta$ values from consecutive possible fall frames and calculate $\sigma_\theta$ using them. This approach differs from the first one since this approach does not include any $\theta$ values other than the possible fall frames. This approaches is the one I used.
\end{enumerate}
\paragraph{}It could be discussed that which approach would result better. The motivation of using this feature is that if there is a large $cMotion$ caused by a walk event there won't be a large deviation in the values of $\theta$ so $\sigma_\theta$ will be low. On the other hand if large $cMotion$ is caused by a fall event then the value of $\theta$'s will change during the fall. This assumption is true if fall event which took place perpendicular to the cameras optical axis. 

\subsubsection{Standard Deviation of $\rho$}
\paragraph{}The calculation of $\sigma_\rho$ is pretty much same with the $\sigma_\theta$. But as I mentioned in \ref{subsection_ellipse_fitting} there seems to be an error in the calculation $\rho$, so no experiments done based on this feature. But its motivation is to detect fall events which took place parallel to the cameras optical axis.

\subsection{Detection Approach}

\subsubsection{Learning Based Detection}
\paragraph{}The first approach I tried is to train a classifier and detect falls using that classifier. The feature is 3 by 1 vector with the values $cMotion$, $\sigma_\theta$, and $\sigma_\rho$. When I was trying this approach I was not aware that $\rho$ values were miss calculated so it didn't performed well. Besides after I gave up on this approach the I've also changed the implementation of the $\theta$ calculation and tried optimize background estimator. Within this changes, after implementing and calculating $\rho$ values correctly this approach could be tried again. \emph{For this approach first calculation technique is used for both $\sigma_\theta$ and $\sigma_\rho$.}

\subsubsection{Thresholding Based Detection}
\paragraph{}After achieving unsuccessful results from the first approach I tend to use the approach mentioned at \cite{Rougier2009}. At this approach frames are eliminated step by step and the resulting frames are fall frames. 
\begin{itemize}
\item Eliminate frames by looking $cMotion$ values. Use the ones left in next elimination step.
\item Eliminate frames by looking $\sigma_\theta$ values. Use the resulting ones as 'real fall candidate'.
\item Apply elimination on 'real fall candidates' by looking their fall duration and the time difference between the falls.
\end{itemize}
\paragraph{}After obtaining the results for a camera, fall events are selected by applying majority voting for multiple cameras. \emph{For this approach second calculation technique is used for $\sigma_\theta$ and $\sigma_\rho$ is not used. It might be logical to apply this approach by using both $\sigma_\theta$ and $\sigma_\rho$. Also using first calculation technique could be some other test. If first calculation is used, then majority voting can be applied for each frame. }  Details of this approach can be found in my SIU paper.
 
\subsection{Dataset}
\paragraph{}The dataset I used in my research has total 192 videos from 8 cameras and 24 scenes. All of the data is annotated so it was kind of easy to calculate performance. Although the videos were not synchronized owner of the dataset delivered an offset matrix to synchronize the videos. Details of the dataset can be found at \cite{Rougier}.

\section{Conclusion}
\paragraph{}The research I've done about this topic was kind of satisfying for me but it was not enough. I'm sure after several meetings and discussions, direction of my researches and studies will become clearer.

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